A hierarchical regime cascade versus the damped random walk on 21 years of GRS 1915+105 and Cyg X-1

Paper B of the Fenocosm arm of the Feno program. A likelihood tournament between a hierarchical regime cascade and the damped random walk on 21 years of real Swift/BAT hard-X-ray monitoring of GRS 1915+105 and Cyg X-1. Abstract. The damped random walk (an Ornstein–Uhlenbeck process) is the default stochastic description of accreting-source light curves. We race it, fairly, against an exact 2k-state Markov-switching multifractal cascade on the public Swift/BAT transient-monitor products for the bright pair, with per-point measurement errors folded into the emission model so the noise model cannot decide the contest, and with stronger linear rivals (CARMA(2,1), OU mixtures) entered beside the DRW. On GRS 1915+105 the cascade wins decisively and out of sample; on Cyg X-1 it does not, and the paper reports the split rather than the win. A parametric bootstrap under DRW truth places the observed statistic beyond every replicate at the ensemble resolution floor, a cadence sweep over a factor of sixteen shows the verdict is not an artifact of daily binning, and a population sweep places the two-source result in the Swift/BAT catalog: the wins scale with multi-stateness rather than with brightness. Caveats carried with the deposit. The multifractal-width statements in this paper are scoped by the program's own null audit: a width is only ever an excess over a matched surrogate null, and record v22 (the scattering-moment re-audit of the same 22 sources) is the controlling measurement for what that excess licenses. Light curves are public archival products fetched at run time and are not part of this deposit. Deposit note. All seven Feno-program repositories are private and remain private, so this deposit is standalone: it carries its own reproduction materials, its metadata contains no repository link, and sibling work is referenced by DOI rather than by repository path. Related Zenodo DOIs cited below are reserved with publication pending. Part of the Feno program. The source repository is private; the reproduction materials for this record are contained in the record itself.